Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×D5×C17×C3⋊D3 |
| unambiguous semidirect product | (C3×D5)⋊(C5×D3×C17) |
| Fitting, socle, Hall | C32×C52×C17 ⋊ C22 |
| derived | C32×C5 ⋊ C22×C5×C17 |
| Hall | C52×C17 ⋊ C2×C3⋊D3 |
| Hall | C32×C52 ⋊ C22×C17 |
| Hall | C32×C17 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×C17×C3⋊D3 |
| Sylow | C32 ⋊ C2×C5×D5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D5×C3⋊D3 |
| commutator, cosocle, hypocenter | C32×C5 | C22×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5×C17 | |
288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1530 |
2040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 378);